LC Oscillations

A radio can tune over the frequency range of a portion of the MW broadcast band (800kHz -1200kHz). If its LC circuit has an effective inductance of 200mH, what must be the range of its variable condenser? 

In a series LR circuit X_L = R and power factor of the circuit is P₁. When capacitor with capacitance C such that X_L = X_C is put in series, the power factor becomes P₂. Calculate P₁/P₂.

A charged 10 microfarad capacitor is connected to an 81 mH inductor. What is the angular frequency of free oscillations of the circuit?  

Calculate the quality factor of a series LCR circuit with L = 2.0 H, C = 2μF and R = 10 Ω. Mention the significance of quality factor in LCR circuit.

An LC circuit contains a 20 mH inductor and a 50 µF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.

(a) What is the total energy stored initially? Is it conserved during LC oscillations?

(b) What is the natural frequency of the circuit?

(c) At what time is the energy stored
(i) completely electrical (i.e., stored in the capacitor)?
(ii) completely magnetic (i.e., stored in the inductor)?

(d) At what times is the total energy shared equally between the inductor and the capacitor?

(e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?

The frequency of the output signal becomes ____________ times by doubling the value of the capacitance in the LC oscillator circuit.

Derive an expression for the impedance of an LCR circuit connected to an AC power supply. Draw phasor diagram.

Calculate the quality factor of a series LCR circuit with L = 4.0 H, C = 1, μF and R = 20 Ω.

Mention the significance of quality factor in LCR circuit.